% Example 6.1
function [y]=banana(x)
 global z1 z2 yg count
 y=100*(x(2)-x(1)^2)^2+(1-x(1))^2;
 z1(count)=x(1); z2(count)=x(2);
 yg(count)=y;
 count=count+1;
end
%
global z1 z2 yg count
count =1;
options=optimset('MaxFunEvals',20)
[b,fval] = fminsearch(@banana,[-1.2, 1],options)
mat=[z1;z2;yg]
%-----------------------------------------------------------------------------
%
% Example 6.2
function value = gp(x)
 x1 = x(1); x2 = x(2);
 value =(1+(x1+x2+1).^2.*(19-14.*x1+3.*x1.^2-14.*x2+6.*x1.*x2+3.*x2.^2))...
   .*(30+(2.*x1-3.*x2).^2.*(18-32.*x1+12.*x1.^2+48.*x2-36.*x1.*x2+27.*x2.^2));
end
%
clear all;
bounds = [-2 2;-2 2];                      % lower- and upper-bounds of design
options.testflag = 1;                                % Global minimum is known
options.globalmin = 3;                         % The value of known global min
options.showits = 1;                                  % Show iteration history
options.tol = 0.01;                                       % Stopping criterion
Problem.f = 'gp';                                    % Objective function name
[fmin,xmin,hist] = Direct(Problem,bounds,options);  % Calling DIRECT algorithm
plot(hist(:,2),hist(:,3))                          % Plot iteration statistics
xlabel('Fcn Evals'); ylabel('f_{min}');
%-----------------------------------------------------------------------------
%
% Example 6.6
function y = Rosenbrock(x)
 y = 100 * (x(1)^2 - x(2))^2 + (1 - x(1))^2;
end
%
rng default % For reproducibility
ndv = 2;
lb = [-3,-3];
ub = [3,3];
[x,fval] = ga(@Rosenbrock,ndv,[],[],[],[],lb,ub)
%
options = optimoptions('ga','MaxGenerations',10000);
[x,fval] = ga(@Rosenbrock,ndv,[],[],[],[],lb,ub,[],[],options)
%-----------------------------------------------------------------------------
%
% Example 6.7
rng default % For reproducibility
nvars = 2;
lb = [-3,-3];
ub = [3,3];
options = optimoptions('particleswarm','SwarmSize',10);
[x,fval,exitflag,output] = particleswarm(@Rosenbrock,nvars,lb,ub,options)
%-----------------------------------------------------------------------------
%
% Example 6.8
function f = objfun(x)
 x1 = x(1);
 x2 = x(2);
 f = (4-2.1.*x1.^2+x1.^4./3).*x1.^2+x1.*x2+(-4+4.*x2.^2).*x2.^2;
end
%
x0 = [0.5 0.5]; % Starting point
lb = [-64 -64];
ub = [64 64];
rng default % For reproducibility
[x,fval,exitFlag,output] = simulannealbnd(@objfun,x0,lb,ub)
%-----------------------------------------------------------------------------